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Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?
4

Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

(OP)
Is it okay to apply the Repetitive Member Factor to a 3-ply wood beam? I have done it in the past based on my reading of the NDS but thought I would inquire here. I have an existing 3-Ply wood beam and since the NDS says 3 or more members in contact or spaced not more than 24", I assume I can use the Cr factor of 1.15. The beam is currently 9% over without the Cr.



RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I don't know about the NDS but here in Canada they call that the system factor, and it applies to regularly spaced members. So if you had 3 ply beams at 24" spacing then sure, but if it's a single beam then definitely not

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Jayrod.
I disagree as I read the code (both NDS and O86) and it states 3 or more members spaced at max 24" (600mm) on center. if you have a 3 ply beam spacing is less the code and therefore the repetitive stress (system factor) applies.

my understanding of this factor is to take into account components that are stronger than code values (#1/#2) grade.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I wouldn't, by my understanding that's not the intent of the Cr factor.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

3 or more members regularly spaced. How can you apply the repetitive member factor to a beam. The wood design manual here has tables for built up beams. I'll have to check tomorrow, but I cant imagine they include an additional 15% bump in capacities just because you went from a 2 ply to a 3.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

We use the Cr factor for 3 ply beams.

Wood tabulated stress values are set up for single members where the statistical variation in wood quality, even when visually rated, can result in lower strength due to random anomalies.

So if you have multiple members, either spaced or bundled, that statistical variation is less powerful and you can have the same assurance of strength with the Cr factor applied to the group as there is to one member.

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RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

agree with JAE
which my interpretation of the code and what I alluded to in my original post.

jae said it better.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

My understanding of the repetitive member factor is identical to JAE's. Statistics.

I would argue that the bump is actually more applicable to a 3-ply whatever than it would be to spaced members. Better odds of better load sharing between 3-ply when you ditch the sheathing acting as a distribution member.

On the other-hand, Jayrod12 is our reigning tip-master / demigod of the week. So there's that.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Interesting thread from 2008 that discusses this: http://www.xiannvgo.com/viewthread.cfm?qid=213584

JAE you seem to have had your position changed. That thread might be why I don't use Cr for single members as that's about the time I started paying attention to engineering tips.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

2
The commentary of the 2005 NDS states:
"The criteria for use of the repetitive member increase are three or more members in contact or spaced not more than 24" and joined by transverse load distributing elements such that the group of members performs as a unit rather than as separate pieces. The members may be any piece of dimensions lumber loading in bending, including studs, rafters, truss chords, and decking, as well as joists."

"The repetitive member increase also applies to an assembly of three or more essentially parallel members of equal size and of the same orientation which are in direct contact with each other. In this case the transverse elements may be mechanical fasteners such as nails, nail gluing, tongue and groove joists, or bearing plates. The required condition is that the three or more members act together to resist the applied moment."

Based on this, I would agree that C_r may be used for a 3-ply beam fastened together.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I don't do much wood design anymore, but I did a fair amount of wood formwork design in a much previous position. Is your 3-ply member one your are having the contractor build up himself, or is it premanufactured? If the latter, I would be wary that it's already been accounted for in the tabulated stresses. (Note, I could be WAY off base, I'm just spit-balling here)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

(OP)
It is an existing beam. The Owner is changing the usage from a flat roof to a deck. The live load goes from 20 psf to 40 psf. That is what is causing the increase. I have always used Cr for 3 ply or more beams but never really sought out guidance on whether I had interpreted it right. Th NDS does say "in contact or spaced not more than 24". It has been my understanding that it is related to statistical difference in relation to variable wood strength.

The NDS also outlines example members but fails to say "beams". I read an article once that stated it applied to beams but cannot recall what the article was. The plys are mechanically connected as required.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I was in a 70 year old house yesterday that had a 4x8 beam spanning 10 ft holding up 9' trib of floor and 12' trib of roof. It was sagging 2". Am I going to worry about a 15% overstress in a beam - not really.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Canadian wood design manual
2x10 SPF single member capacity 4.1 kNm
2x10 SPF Case 2 (repetitve member) capacity 5.72 kNm

SPF 2 ply 2x10 beam capacity 8.99 kNm (so 1.1 * Single member * 2)
3 ply 13.5 kNm (again 10% increase)

this 10% increase continues to 4 and 5 plys.

In my mind, this tells me that they are not taking repetitive member into account since the same 10% increase applies to a 2 ply beam.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

TehMightyEngineer,
Ha! You caught me!
Yes, I recall that post and after reading through it realized that a built-up beam is definitely "repetitive".

Old dogs can and do learn new tricks I guess.

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RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Nice find StrucDesignEIT! That seems to completely address this. I looked for this last night but apparently didn't read the commentary.

Well, guess I'll also start using Cr in my multi-ply beams now.

JAE: Well, that was over 10 years ago now.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

It appears the Canadian code takes a much different approach, applying a 1.4 repetitive member factor, but only a 1.1 factor for multiple ply beams. Hmm...perhaps because repetitive members separated by some space have greater ability to develop load capacity at different deflections? I guess I can see a scenario where some joists are less stiff than others, so require greater deflection to develop their full capacity. With laminated plies, this would not be able to occur. That's the only reason I can think of for the differences.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

(OP)
Jayrod,

I am not familiar with the Canadian Wood Design but what is the 10% you are citing?

Also, the Case 2 you are referring to shows about 40% increase over your single member. Is that the repetitive factor for the Canadian code?

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Ron,

Yes, so the single member is used for a straight up single 2x member that violates the requirements for repetitive member. But up here we call repetitive member "System Cases" where our increase is 40% over a stand-alone single joists however this is subject to a minimum of 3/8" board sheathing or 5/8" decking to qualify(i.e. System case 2).

That being said, we also have System Case 1 members in the joist design area that indicates "Case 1 systems are composed of three or more essentially parallel members spaced no more than 24" apart and are arranged so they mutually support the load. However, Case 1 systems lack the sheathing and fastening requirements to qualify as Case 2 systems; or they may include a more complex structural component such as a wood truss." Which when you go on to read it says if you qualify for case 1 but not case 2, you multiple the single member values by 1.10. so there may be some validity to applying to beams.

What I was saying is when comparing the capacity of 2, 3, 4, and 5 ply beams to the single member capacity there is a 10% increase over just taking the single member capacity and multiplying by 2, 3, 4 or 5.

In the Canadian code however, Mr is a function of bending stress, section modulus, and two factors Kz (Size factor) and KL (Lateral stability factor). Digging deeper, it appears they apply the 1.1 factor to the bending stress for beams prior to publishing the number. So we never see a "repetitive member factor" in our beam design formulae if you just pick the beam bending stress from the tables.

Long winded story cut short (TL;DR), In Canada even 2 ply beams have a repetitive member factor included, however it is only a 10% increase for all built up beams. The repetitive member factor for joists with floor sheathing is a 40% increase.

Quote (KootK)

On the other-hand, Jayrod12 is our reigning tip-master / demigod of the week. So there's that.
Twice in my tenure, and I'm pretty sure I just got lucky.

edited for clarity

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Quote (Jayrod12)

Twice in my tenure, and I'm pretty sure I just got lucky.

I tend to pick up the title over Christmas each year when smarter/better men are spending time with their families.

Code intentions aside, I've always found it odd that load sharing increases are a thing at all in wood construction. In my opinion, load sharing implies redistribution which implies a ductile failure mechanism of the member sharing its load. As far as I know, most wood failure mechanism are pretty brittle. To a vastly milder degree, it's like bolting three layers of glass together to form a beam and slapping a stress increase on that for variability / sharing. In glass, you're not only not taking an increase, your're probably designating a ply sacrificial. Not that I'm suggesting anybody do that for built up 2x10's.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I feel that you get load sharing from the inherent flexibility of wood members. the deflections at failure are quite in comparison to the relative difference in member elevations. But perhaps that's just me justifying the increase for the sake of keeping it.

And considering this increase only applies to the bending resistance of members and not to the more drastic shear failure and/or connection failure, I can get a bit on board with that.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I suspect it's less about failure modes and more about the inherent variability of wood and the established allowable stresses. To use your glass analogy, it's 3 glass plies where random glass plies have much more strength than anticipated. Also, wood failure in bending is, to some degree, not entirely brittle. Overloaded wood joists tend to deflect heavily, then crack and split, and then redistribute some or all of their load to stronger neighboring joists prior to the whole thing coming down (based on a few roof failures I've investigated).

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Quote (jayrod12)

And considering this increase only applies to the bending resistance..

Quote (TME)

Also, wood failure in bending is, to some degree, not entirely brittle.

Wood bending failure is really wood tension failure. And I don't believe that wood tension failure is particularly ductile. Ever been involved in bending some wood members for aesthetics? You basically have to steam the crap out wood before bending it or it blows up when bent. This is why.

Quote (TME)

To use your glass analogy, it's 3 glass plies where random glass plies have much more strength than anticipated. Also, wood failure in bending is, to some degree, not entirely brittle.

I realize that it's about material variability and that precisely the problem (it is with glass too). If you've got three plies and one is weak, that one breaks and your left with two good plies, not two good plies and one, still functioning crappy ply.

There might be some serviceable logic in claiming that the strongest plies are also the stiffest plies and, therefore, the strongest plies will draw load before that load is seen by the crap plies. A demonstrable relation between stiffness and strength certainly exists but seems a little sketchy when employed this way.

I can see where this is going so I'll repeat: I've no objection to anybody using Cr. This is theoretical musing for sport.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

One data point for consideration: Link. 50 sec in if you're not down for watching paint dry on a Friday afternoon.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Look at this bad-ass yield plateau from the same test. We should start dong special moment frames in wood.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Although, given the nature of the situation, this one based on a defect is probably more representative: Link Failure appears to progress from initiation to completion at roughly the speed of sound.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

(OP)
The failures denoted in those tests have the appearance of a brittle fracture but the intensity of the brittleness does not appear as severe at is would for unreinforced concrete or masonry. I have been around wood members when they literally broke. You do get some warning and then they pretty much shatter. You hear something is going wrong right before they Rice Krispie on you.

What do you think is occurring at about 10 kN where the curvature changes on the graph? I have tried watching the video slow to see if that is where you can start seeing the bearing plates compressing the wood.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Quote (Ron247)

What do you think is occurring at about 10 kN where the curvature changes on the graph

Vastly out of my depth on this but when has that stopped me:

- I think it's all about the tension fibers being... fibrous.

- Initially, you get stiffening as the fibers align themselves for maximum load resistance.

- At 10 kN, the fibers are done straightening and maybe start doing something like necking whereby your effective cross section, and thus stiffness, is reducing.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

(OP)
Kootk,

That seems to be a rational cause and effect. My first thought was the bearing but each time I watched it, the bearing depression appeared after about half the sag, not at the third point of the sag.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Yeah, based on the relative difference between available compression stress and tension stress, I doubt that minor damage on compression side would make that much of a difference.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

My theory was partly informed by my own, recent medical adventures. I partially tore a rotator cuff back in November. My longtime doctor, knowing what I'm like, drew me a sketch of how things would unfold. With rest, my old man shoulder muscle would knit itself back together. Or at least try. But post knitting, the fibers would be somewhat randomly oriented relative to load. Five degrees off here, fifteen degrees off there. Apparently, with some strategic stretching (load), the fibers would eventually align themselves more efficiently relative to the loading axis. However, if I worked the muscle too hard, too soon, the reduced effective tissue cross section would stretch out and eventually reach a tipping point where you'd have a cascading/unzipping failure. And since I'm too old and non-olympic for anyone with an insurance policy to risk surgery on me, I'd just have to learn to brush my hair with my left hand.

To an extent, all living tissue must exhibit some commonality.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Quote (KootK)

And I don't believe that wood tension failure is particularly ductile.

Reconsidering, you're probably correct. Though in your video link they have a fairly small depth to span ratio. I'd surmise with a more reasonable span of a typical floor beam you would see excessive deflection or perhaps some lateral-torsional mode before ultimate failure. In short, I'd say my position is that you would get greater stiffness out of the stronger members and we're only talking about an assumed 15% overstrength.

I also noted that the video with the defect they had a some cracking prior to failure. This was minimally ductile in my mind.

Quote (KootK)

I think it's all about the tension fibers being... fibrous.

I'd agree with your assessment.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Quote (TME)

I'd surmise with a more reasonable span of a typical floor beam you would see excessive deflection or perhaps some lateral-torsional mode before ultimate failure.

For the purpose of sussing out Cr, I think that it's a logical error to give any consideration to what may or may not happen along the path to maximum, pre-failure bending capacity. That, because Cr is entirely about what is happening at the particular moment in time that maximum capacity is reached. Cr doesn't care about the path followed to reach that point in time.

Things such as excessive deflection and LTB that might well precede bending failure in a practical structure are great in terms of providing warning to the villagers but, in my opinion, they affect ultimate bending capacity, and therefore the Cr discussion, not at all.

When it comes to showing whether or not a bending failure is brittle, I feel that the videos show the only thing that would be meaningful to show: a bending failure. And the only way to accomplish that would have been to supply proportions that would produce that result.

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

I should clarify my comments on excessive deflection and LTB. I meant that the "weak" ply would have cracking or defects such that it deflects more (excessive deflection) or begins LTB (if not restrained in a multi-ply beam) or some other failure mode due to cracking and reduced section sooner than it's neighbors. Basically providing rational for my argument that the "weak" ply would distribute 15% of it's load to adjacent plys just prior to failure.

Again though, I do ultimately agree with you. Bending failures in wood are sudden and brittle and don't have a nice yield plateau like steel. Thus redistribution in the idealized sense is likely impossible and the 15% Cr factor is probably just as much a "rule of thumb" as a rational argument for material variability.

I suppose one other consideration is that defects and other such things in wood are likely not located strictly at the point of maximum flexural stress. Thus, you could have a ply fail at a defect at the 1/3 span point (for example), split and turn into effectively a notched or tapered section, while still having full depth at the point of maximum stress for the whole multi-ply beam. I believe this would result in a redistribution of stress even with a brittle failure.

Ian Riley, PE, SE
Professional Engineer (ME, NH, VT, CT, MA, FL) Structural Engineer (IL, HI)

RE: Repetitive Member Factor (1.15) applied to 3-Ply Wood Beam?

Rooting around online, I found this from a HUD design guide.

- Higher values have been proposed.

- Testing has been performed, particularly on built up headers.

- Some good references there for anyhow who might be feeling super keen. I'd be interested to know the nature of the testing.









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